Tan 570 Degrees

Sin, Cos, Tan, Cot of an Angle
Function
Angle (°)

What is tan 570°?

Answer

tan 570° =
√3/3 ≈ 0.5774

Angle in radians: 570° = 19π/6. 570° = 360° + 210° — a full turn plus 210°, quadrant III, where tangent is positive.

≈ — rounded to 4 decimal places.

tan 570° = tan(570° − 360°) = tan 210°

tan 210° = tan(180° + 30°) = tan 30° = √3/3

tan 570° = sin 570° / cos 570° = (−1/2) / (−√3/2) = √3/3

Half of an equilateral triangle with side 1: the hypotenuse is 1 and the leg opposite 30° is 1/2.

tan 30° = (1/2) / (√3/2) = 1/√3 = √3/3

xyOP

P(cos 570°, sin 570°) ≈ (−0.8660, −0.5)

T(1, tan 570°) ≈ (1, 0.5774) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

+1 turn: the drawing shows 210°.

All four functions of 570°
FunctionExact valueDecimal
sin 570°−1/2−0.5
cos 570°−√3/2≈ −0.8660
tan 570°√3/3≈ 0.5774
cot 570°√3≈ 1.7321

Reference angle: tan 30° = √3/3

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
390°√3/3
400°≈ 0.8391
450°undefined
540°0
570°√3/3
690°−√3/3
720°0

FAQ

What is tan 570°?

tan 570° = √3/3 ≈ 0.5774

How to remember sin 30°, sin 45° and sin 60°?

Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: tan 570° = √3/3 ≈ 0.5774.

Why does a calculator show 4.9569 for tan 570?

The calculator is in radian mode (RAD): it takes tan 570 as the tangent of 570 radians, tan 570 rad ≈ 4.9569. Switch it to degrees (DEG): tan 570° = √3/3 ≈ 0.5774. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also